Non-local elasto-viscoplastic models with dislocations in finite elasto-plasticity. Part II: Influence of dislocations in crystal plasticity

Abstract

We emphasize the consequences that follow from the constitutive framework of second-order finite elasto-plasticity, with tensorial and scalar measures of dislocations, developed in Part I of this paper, which was restricted to the multislip flow rule for plastic distortion, specifically used in crystal plasticity. The micro-balance equation proposed by Gurtin is obtained. The non-local evolution equations for the plastic shear and scalar dislocation density are built into the appropriate slip system and are compatible with the reduced dissipation inequality. The activation condition is dependent on Noll’s dislocation density tensor, or on the curl of the plastic distortion, and there is a force-like coupling term containing the gradient of the scalar dislocation density, which also produces internal power in conjunction with the rate of plastic distortion. The evolution equation for the scalar dislocation density is non-local and is expressed as a diffusion equation. To study the influence of the non-local description of the scalar dislocation densities on the elasto-plastic behaviour, we consider as an example a layer of an elasto-plastic material when a single slip system could be activated, in a simple shear stress-controlled problem, within a simplified non-local viscoplastic model. For a hardening material, a drastically non-smooth change in the plastic shear and the components of the deformation gradient is emphasized.